On the Absence of Bound States for a Planar Massless Brown–Ravenhall-Type Operator

We address the question of the existence of bound states for a suitably projected two-dimensional massless Dirac operator in the presence of a Bessel–Macdonald potential (also known as K_0 -potential potential), raised in De Lima (Eur Phys J B 93:187, 2020). Based on Relativistic Hardy Inequality, we prove that this operator has no bound states if γ⩽γ _crit (subcritical region), where γ is a coupling constant.